Assume that we set a flat prior for (, ), i.e. p(, ) 1. Write down the posterior distribution as a function of and . 2. Write a Metroplis algorithm to sample from this posterior distribution. Report the step size that you choose, number of iterations, effective sample size of your algorithm. For convenience, you can set the inital values of and to be 0.8 and 7.7 respectively. 3. A parameter of common interest in bioassay studies is the LD50the dose level at which the probability of death is 50%. In our logistic model, a 50% survival rate means LD50: E(yi|ni) = logit1( xi) = 0.5; thus, xi = logit(0.5) = 0, and the LD50 is xi = /. Summarize and visualize the posterior distribution for LD50. 2